SPECIAL VALUES OF JACOBI THETA FUNCTION
In this post we well prove the following results Click here to see the proof.
Posts
Alternating reciprocal of cosh infinite sum
Today we will prove the following result seen in this post Click here to see the proof
Infinite sum reciprocal of cosh(n \pi)
In today´s blog entry we will prove the following infinte sum Click here to see the proof.
Variation on Binet´s second formula
In this post we will prove the following result We start by recalling Hermite´s integral representation of the Hurwitz zeta function (proved here ) (1) We may rewrite it in a slightly different way which facilitates some calculations, to this end we start with the following lemma: Lemma: Proof: We can therefore rewrite (1) as (2) Differentiating (2) w.r. to s we obtain (3) Letting and using the logarithmic representation of arctan we obtain rearranging terms we get: Now let to obtain Which concludes the proof. Note: In the proof above we used the following previously established results Proved here Proved here Proved here